MULTIGRID METHODS TO ACCELERATE CONVERGENCE OF ELEMENT-BY-ELEMENT SOLUTION ALGORITHMS FOR VISCOUS INCOMPRESSIBLE FLOWS

The use of iterative solvers for large systems of equations results in a slow convergence rate after the small wave length error components are resolved. For a fixed convergence tolerance limit, the error resol ution capability of an iterative solver is a function of the mesh dens ity. Two iterative solvers (GMRES and ORTHOMIN), which utilize the ele ment-by-element (EBE) data structure of the finite element mesh, are s tudied to demonstrate this behavior. A significant improvement in the accuracy of the solution and the rate of convergence is achieved for t hese iterative solvers by using a successive mesh refinement scheme (l ike in a multigrid method). This approach is found to better resolve b oth the large and the small scale flow phenomenon for a fine mesh whil e satisfying the convergence criterion in a fraction of the CPU time r equired by the standard iterative methods. An iterative penalty finite element model is used to solve the governing equations for laminar, i ncompressible, isothermal fluid flows. The solution accuracy and CPU t ime savings are demonstrated for two sample problems.